Answer: p=9.7
Step-by-step explanation:
40p+ 10.5p=489.85
50.5p=489.85
9.7=p
Answer:
13
Step-by-step explanation:
Using long division, you can multiply each given value by 100 to eliminate the decimals:
2.08x100=208
0.16x100=16
OR (calculator method)
2.08÷0.16=13
You must divide the amount of food per cat by the total amount of food available to determine how many cats can be fed. This division can be done using a calculator.
OR
10 times 'x' is 10 times whatever the value of 'x' is. I hope that makes sense.
Answer:
the common ratio is either 2 or -2.
the sum of the first 7 terms is then either 765 or 255
Step-by-step explanation:
a geometric sequence or series of progression (these are the most common names for the same thing) means that every new term of the sequence is created by multiplying the previous term by a constant factor which is called the common ratio.
so,
a1
a2 = a1×f
a3 = a2×f = a1×f²
a4 = a3×f = a1×f³
the problem description here tells us
a3 = 4×a1
and from above we know a3 = a1×f².
so, f² = 4
and therefore the common ratio = f = 2 or -2 (we need to keep that in mind).
again, the problem description tells us
a2 + a4 = 30
a1×f + a1×f³ = 30
for f = 2
a1×2 + a1×2³ = 30
2a1 + 8a1 = 30
10a1 = 30
a1 = 3
for f = -2
a1×-2 + a1×(-2)³ = 30
-10a1 = 30
a1 = -3
the sum of the first n terms of a geometric sequence is
sn = a1×(1 - f^(n+1))/(1-f) for f <>1
so, for f = 2
s7 = 3×(1 - 2⁸)/(1-2) = 3×-255/-1 = 3×255 = 765
for f = -2
s7 = -3×(1 - (-2)⁸)/(1 - -2) = -3×(1-256)/3 = -3×-255/3 =
= -1×-255 = 255
The point-slope form:
m - slope
(x₁, y₁) - point
The formula of a slope:
We have the points (-2, 7) and (1, 1). Substitute:
<em>point-slope form</em>
<em> slope-intercept form</em>
<em>standard form</em>
